A novel approach to find analytical solutions for Oldroyd 6-constant fluid

Abstract

The study is concerned with the application of a novel idea used to find analytical solutions of a nonlinear boundary value problem that arises in channel flow problems. The velocity profile of a viscoelastic fluid between two planes is obtained with both slip and no-slip boundary conditions. We present analytical solutions on classical problems – the Poiseuille flow, and the generalized Couette flow of a viscoelastic fluid between two parallel planes. The viscoelastic fluid is modeled by an Oldroyd 6-constant fluid, giving rise to a highly nonlinear ordinary differential equation. This equation has been solved via a novel approach by reducing the differential equation to a cubic algebraic equation, giving rise to a non-recursive series solution to the equation. Finally, after the solution of the general differential equation is given Newton’s Method is used for faster convergence to solve the equation in the case of three common boundary conditions.